We detail below several examples of virus propagation models being used for characterizing the transmission and spread of diseases. These compartmental build upon the early work of Kermack and McKendrick [1]}. Thus, all individuals in a population (in our case, the nodes in a network) are in one of the states, either susceptible (S) or infected (I). Based on the viral propagation, they can move to other states like Exposed (E), Recovered (R), or Deceased (D). For example, the SIR model involves individuals being in one of three states, (S), (I) or (R) and transitioning between the states probabilistically. Typically, the vast majority of nodes are present in the susceptible state (S), in which they might contrast the disease. The exposed state (E) is used to indicate a node that has been exposed to the disease, but could be asymptomatic during an incubation period and is not capable of infecting others. In contrast, the infected state (I) indicates a node that is capable of infecting others. The (R) recovered state implies permanent immunity.
There are further extensions possible, e.g. adding infants who have maternal antibodies (state M) that provide passive immunity. See [2]} or [3]} for an overview and survey of these models. These models have been extensively used in epidemiological studies to characterize disease dynamics as detailed in Table REF , including measles, influenza and COVID-19.
